{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:17Z","timestamp":1753893857022,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>To estimate the lower bound for the chromatic number of a graph $G$,\u00a0 Lov\u00e1sz associated a simplicial complex\u00a0 $\\mathcal{N}(G)$ called the neighborhood complex and related the topological connectivity of $\\mathcal{N}(G)$ to the chromatic number of $G$. More generally he proved that the chromatic number of $G$ is bounded below by the topological connectivity of $\\mathcal{N}(G)$ plus $3$. In this article, we consider the graphs of maximal degree at most $3$ and $4$-regular circulant graphs. We show that each connected component of the neighborhood complexes of these graphs is homotopy equivalent either to a point, to a wedge sum of circles, to a wedge sum of $2$-spheres $S^2$, to $S^3$, to a garland of $2$-spheres $S^2$ or to a connected sum of tori.\u00a0<\/jats:p>","DOI":"10.37236\/7549","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:08:42Z","timestamp":1578640122000},"source":"Crossref","is-referenced-by-count":2,"title":["Homotopy Type of the Neighborhood Complexes of Graphs of Maximal Degree at most $3$ and $4$-Regular Circulant Graphs"],"prefix":"10.37236","volume":"26","author":[{"given":"Samir","family":"Shukla","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,4,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p4\/7816","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p4\/7816","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:15:22Z","timestamp":1579234522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,5]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7549","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,4,5]]},"article-number":"P2.4"}}